International Journal of Fracture

, Volume 194, Issue 2, pp 93–106 | Cite as

The influences of Coulomb tractions on static and dynamic fracture parameters for semi-permeable piezoelectric cracks

  • Jun Lei
  • Pengbo Sun
  • Chuanzeng Zhang
  • Felipe Garcia-Sanchez
Original Paper


In this paper, the influences of the induced Coulomb tractions on the static and dynamic crack-tip fracture parameters of semi-permeable piezoelectric cracks are studied and discussed. The static crack problems are solved by a static dual boundary element method (BEM), while the corresponding crack problems under dynamic impact loading are numerically analyzed by a time-domain BEM considering the inertial effects. In the numerical implementation, a collocation method is applied for the spatial discretization together with a quadrature formula for the temporal discretization. An iterative scheme based on the quasi-Newton method is adopted to solve the corresponding non-linear boundary-value problem resulted from the semi-permeable electric boundary conditions and the induced Coulomb tractions on the crack-faces. The crack-tip facture parameters involving the field intensity factors, the energy release rate and the mechanical strain energy release rate are evaluated by a displacement extrapolation method. Some examples are presented to compare the effects of the Coulomb tractions on the static and dynamic fracture parameters.


Coulomb tractions Semi-permeable cracks Fracture parameters Static and dynamic loading Piezoelectric materials 



This work is supported by the Natural Science Foundation of China under Grant No. 11472021, and the German Research Foundation (DFG) under the Project No. ZH 15/14-1, which are gratefully acknowledged.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Jun Lei
    • 1
  • Pengbo Sun
    • 1
  • Chuanzeng Zhang
    • 2
  • Felipe Garcia-Sanchez
    • 3
  1. 1.Department of Engineering MechanicsBeijing University of TechnologyBeijingPeople’s Republic of China
  2. 2.Department of Civil EngineeringUniversity of SiegenSiegenGermany
  3. 3.Departamento de Ingeniería Civil, de Materiales y Fabricación, E.T.S. de Ingenieros IndustrialesUniversidad de MálagaMálagaSpain

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